Financial Integration, Financial Development, and Global Imbalances

Financial Integration, Financial Development, and Global ImbalancesAuthor(s): Enrique G. Mendoza, Vincenzo Quadrini, and José‐Víctor Ríos‐RullSource: Journal of Political Economy, Vol. 117, No. 3 (June 2009), pp. 371-416Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/10.1086/599706 .

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371

[ Journal of Political Economy, 2009, vol. 117, no. 3]� 2009 by The University of Chicago. All rights reserved. 0022-3808/2009/11703-0001$10.00

Financial Integration, Financial Development,and Global Imbalances

Enrique G. MendozaUniversity of Maryland and National Bureau of Economic Research

Vincenzo QuadriniUniversity of Southern California, Centre for Economic Policy Research, and National Bureau ofEconomic Research

Jose-Vıctor Rıos-RullUniversity of Minnesota, Federal Reserve Bank of Minneapolis, Centro de Analysis y EstudiosRıos Perez, Centre for Economic Policy Research, and National Bureau of Economic Research

Global financial imbalances can result from financial integration whencountries differ in financial markets development. Countries withmore advanced financial markets accumulate foreign liabilities in agradual, long-lasting process. Differences in financial developmentalso affect the composition of foreign portfolios: countries with neg-ative net foreign asset positions maintain positive net holdings of non-diversifiable equity and foreign direct investment. Three observationsmotivate our analysis: (1) financial development varies widely evenamong industrial countries, with the United States on top; (2) thesecular decline in the U.S. net foreign asset position started in theearly 1980s, together with a gradual process of international financial

We would like to thank Manuel Amador, David Backus, Luca Dedola, Linda Goldberg,Pierre-Olivier Gourinchas, Gita Gopinath, Ayse Imrohoroglu, Patrick Kehoe, KyungsooKim, and Alessandro Rebucci for insightful comments and Gian Maria Milesi-Ferretti andPhilip Lane for sharing their cross-country data on foreign asset positions. We also thankparticipants at several universities and conferences. Financial support from the NationalScience Foundation is gratefully acknowledged: Quadrini with grant SES-0617937 andRıos-Rull with grant SES-0079504. The views expressed herein are those of the authorsand not necessarily those of the Federal Reserve Bank of Minneapolis or the FederalReserve System.



372 journal of political economy

integration; (3) the portfolio composition of U.S. net foreign assetsfeatures increased holdings of risky assets and a large increase in debt.

I. Introduction

At the end of 2006, the current account deficit of the United Statesreached 1.6 percent of the world’s GDP, the largest in the country’shistory. Continuing a trend that started in the early 1980s, the U.S. netforeign asset (NFA) position fell to �5 percent of the world’s output.During this period, the U.S. foreign asset portfolio also changed dra-matically: net equity and foreign direct investment (FDI) climbed toone-tenth of U.S. GDP, whereas net debt obligations increased sharplyto about one-third of U.S. GDP.

These unprecedented global imbalances are the focus of a large andgrowing literature. Some studies argue that the imbalances resulted fromeconomic policy misalignments in the United States and abroad,1

whereas others argue that they were caused by events such as differencesin productivity growth, business cycle volatility, demographic dynamics,a “global savings glut,” or valuation effects.2 To date, however, a quan-titatively consistent explanation of both the unprecedented magnitudeof the changes in NFA positions and the striking changes in their port-folio structure has proven elusive.

In this paper we show that both of these phenomena can be explainedas the equilibrium outcome of financial integration across countrieswith heterogeneous domestic financial markets. This is a relevant hy-pothesis because the reforms that integrated world capital markets start-ing in the 1980s were predicated on their benefits for efficient resourceallocation and risk sharing across countries, ignoring the fact that do-mestic financial systems differed substantially, and these differences per-sist today despite the globalization of capital markets. In short, financialintegration was a global phenomenon, but financial development wasnot.

The empirical motivation for our analysis derives from three keyobservations.

1. There is a high degree of heterogeneity in domestic financial markets acrosscountries, and these differences remain largely unaltered despite financial glob-

1 See, e.g., Obstfeld and Rogoff (2004), Summers (2004), Blanchard, Giavazzi, and Sa(2005), Roubini and Setser (2005), and Krugman (2006).

2 See Backus et al. (2005), Bernanke (2005), Croke, Kamin, and Leduc (2005), Haus-mann and Sturzenegger (2005), Henriksen (2005), Attanasio, Kitao, and Violante (2006),Cavallo and Tille (2006), Engel and Rogers (2006), Fogli and Perri (2006), Chakrabortyand Deckle (2007), Deckle, Eaton, and Kortum (2007), Ghironi, Lee, and Rebucci (2007),Gourinchas and Rey (2007), Lane and Milesi-Ferretti (2007), Prades and Rabitsch (2007),Caballero, Farhi, and Gourinchas (2008), and McGrattan and Prescott (2008).



financial integration 373

alization and financial development. Figure 1A plots the financial devel-opment index constructed by the International Monetary Fund for in-dustrial countries (see IMF 2006). The index shows that there are largedifferences even among advanced economies, with the United Statesranked first. In addition, the gaps of other industrial countries relativeto the United States did not change significantly between 1995 and2004. Similar features are evident in another index of financial devel-opment constructed by Abiad, Detragiache, and Tressel (2008) for in-dustrial and emerging economies for the 1973–2002 period. As shownin figure 1B, while financial liberalization progressed in both OECDand emerging economies over the last 30 years, the gap between thetwo groups of countries has not changed.

2. The secular decline of the NFA position of the most financially developedcountry—the United States—began roughly at the same time as the financialglobalization process, in the early 1980s. Figure 2A shows the Chinn-Itofinancial openness index for the United States, the industrial countriesexcluding the United States, and all countries except the United States.Capital markets in the United States have been relatively open to therest of the world throughout the last three decades. Most of the othercountries started opening their capital accounts gradually since the early1980s. Figure 2B shows that this process of financial integration pro-duced a worldwide surge in gross stocks of foreign assets and liabilities.

3. The decline in the U.S. NFA position was accompanied by a marked changein the portfolio composition of foreign assets of all countries. Figure 3 plots thetwo broad components of the total NFA positions: net debt instruments(including international reserves) and net portfolio equity and FDI. Theplots show that the United States increased net holdings of risky assets(portfolio equity and FDI) and reduced net holdings of riskless assetsinto a very large negative position. Other industrial countries changednet holdings of risky assets in a similar way but hardly changed holdingsof riskless assets. The emerging economies reduced net holdings of riskyassets and increased holdings of riskless assets. See also Gourinchas andRey (2007), Lane and Milesi-Ferretti (2007), and Curcuru, Dvorak, andWarnock (2008).

We build a model suitable for empirical analysis in which we take asgiven observations 1 and 2 to explain the facts highlighted in observation3 (i.e., the changes in NFA positions and in their portfolio structure).In our model, countries are inhabited by ex ante identical agents whoface two types of idiosyncratic shocks: endowment and investmentshocks. Financial development is defined by the extent to which a coun-try’s legal system can enforce financial contracts among its residents sothat they can use these contracts to insure against idiosyncratic risks.

In our model, the state of development of a country’s legal system isrepresented by the fraction of individual income that the country’s



374

Fig. 1.—Indices of financial markets heterogeneity. A, Financial index score for ad-vanced economies (data from IMF [2006]). Open bars p 1995; black bars p 2004. B,Index of financial liberalization (data from Abiad et al. [2008]). Solid line p OECDcountries; dashed line p emerging economies. See Appendix A for definitions of thevariables.



375

Fig. 2.—Indices of financial openness. A, Index of capital account openness (data fromChinn and Ito [2005]). Solid line p United States; dashed line p OECD countries exceptUnited States; dotted line p all countries except United States. B, Gross stock of foreignassets and liabilities (data from Lane and Milesi-Ferretti [2007]). Solid line p UnitedStates; dashed line p OECD countries except United States; dotted line p emergingeconomies. See Appendix A for definitions of the variables.



Fig. 3.—Net foreign asset positions in debt instruments and risky assets. A, NFA in debtand international reserves. B, NFA in portfolio equity and FDI. Data from Lane and Milesi-Ferretti (2007). Solid line p United States; dashed line p OECD countries except UnitedStates; dotted line p emerging economies. See Appendix A.




residents can divert from creditors. In autarky, countries with betterlegal systems, or that are more financially developed, attain lower av-erage wealth-to-income ratios and higher interest rates. Upon financialliberalization, interest rates are equalized across countries, but the gapin their wealth-to-income ratios widens significantly. The latter occursafter a protracted process that takes several years to be completed andthat is responsible for large, sustained declines in NFA positions likethe one experienced by the United States. We show that moderate dif-ferences in financial development can easily lead to NFA positions largerthan half of domestic production. Moreover, the adjustment process ofNFA can take more than 30 years.

A second key feature that characterizes the legal systems is that en-forcement is “residence based.” That is, the enforcement of financialcontracts is determined by the law of the country where the agent re-sides. Alternatively, “source-based” enforcement would imply that theenforcement of financial contracts is determined by the law of the coun-try where the incomes are generated. With residence-based enforce-ment, our model can explain not only the change in overall NFA po-sitions but also their portfolio structure (i.e., the most financiallydeveloped country has a large, negative NFA position, but it also haspositive net holdings of nondiversifiable equity and large, negative netholdings of riskless bonds). Our quantitative analysis shows that this isindeed the case for economies that resemble the United States vis-a-visthe rest of the world. Moreover, a three-country extension of the modelaccounts for both the large negative NFA position of the United Statesand the differences in portfolio structures across the United States, otherindustrial countries, and emerging economies.

The premise that differences in domestic financial markets can pro-duce external imbalances has precedent in the literature. Willen (2004)studied the qualitative predictions of a two-period endowment-economymodel with exponential utility and normal-i.i.d. (independent and iden-tically distributed) shocks. He showed that, under incomplete markets,trade imbalances emerge because of reduced savings by the agents re-siding in countries with “more complete” asset markets. Our modelembodies this mechanism but differs in two key respects. First, we allowfor endogenous production with “production risks,” which is necessaryfor explaining the composition of asset portfolios. Second, we study aninfinite horizon model with standard constant relative risk aversion pref-erences, exploring both the qualitative and quantitative predictions ofthe model.

Caballero et al. (2008) also emphasize the role of heterogeneousdomestic financial systems in explaining global imbalances, but using amodel in which financial imperfections are captured by a country’sability to supply assets in a world without uncertainty. In our framework,




instead, financial imperfections have a direct impact on savings and,therefore, on the demand for assets. Uncertainty is crucial in our frame-work: without risk there are no imbalances, even if financial marketsare heterogeneous. The two papers also differ in the main driving forcesof global imbalances. In Caballero et al., the imbalances are generatedby differential shocks to productivity growth and/or to the financialstructure of countries. Our explanation relies instead on the integrationof capital markets, given the differences in the characteristics of do-mestic financial markets.

Our work is also related to studies that investigate global imbalanceswith quantitative dynamic general equilibrium models (see Hunt andRebucci 2005; IMF 2005; Faruqee, Laxton, and Pesenti 2007). In thesestudies, global imbalances emerge as the outcome of a combination ofexogenous shocks, such as a permanent increase in the U.S. fiscal deficit,a permanent decline in the rate of time preference in the United States,and a permanent increase in foreign demand for U.S. financial assets.In contrast, our model predicts a reduction in U.S. savings and anincrease in the foreign demand for U.S. assets endogenously, after fi-nancial integration, because of the different characteristics of the U.S.financial system. This occurs even if all countries have identical pref-erences, resources, and production technologies.

The rest of the paper is organized as follows: Section II describes abasic two-country framework that we use to characterize analytically thekey theoretical results. Section III extends the basic model to make itsuitable to map it to the data. Section IV conducts the quantitativeanalysis and identifies the winners and losers from financial liberaliza-tion. Section V compares the implications of our assumption of resi-dence-based enforcement with different variants of source-based en-forcement. We find that if enforcement of financial contracts involvinginternational payments is fully source based in all countries, our modelstill accounts for large negative positions in NFA and riskless assets inthe most financially developed country, but it does produce positive netholdings of risky assets in that country. However, mixed environmentsthat combine source- and residence-based enforcement, which are likelyto be more realistic, support equilibria with positive net foreign equitypositions in the most financially developed country. Section VI extendsour notion of financial development to allow for differences in borrow-ing limits. This allows the model to account for differences in portfoliostructures across the United States, other industrial countries, andemerging economies. This section also shows that the results can beextended to the case in which there are differences in growth rates andincome volatility across countries. Section VII presents conclusions.




II. A Model of Financial Globalization with Financial Heterogeneity

We now describe a simple version of the model that illustrates the keyproperties analytically. These properties are preserved in the generalsetup we will use in the quantitative analysis.

Consider an economy composed of two countries, , inhabitedi � {1, 2}by a continuum of agents of total mass one. Agents maximize the ex-pected lifetime utility , where is consumption at time t� tE � bU(c ) ct ttp0

and b is the discount rate. The utility function is strictly increasing andconcave with and .′′′U(0) p �� U (c) 1 0

Each country is endowed with a unit of a nonreproducible, inter-nationally immobile asset, traded at price . This asset can be used byiPt

each agent in the production of a homogeneous good, with a one-periodgestation lag. Thus, the individual production function is ,ny p z kt�1 t�1 t

where is the quantity of the asset used at time t, is a project-k zt t�1

specific idiosyncratic discrete shock, and is the output produced atyt�1

time . We refer to as an investment shock because it determinest � 1 z t�1

the ex post return on the investment .kt

We assume that ; that is, individual production displays decreas-n ! 1ing returns to scale. This property derives from the assumption thatproduction also requires the input of managerial or organizational cap-ital, of which agents have limited supply. Managerial capital cannot bedivided among multiple projects, but it is internationally mobile. There-fore, with capital mobility agents can choose to operate at home, buyingthe domestic productive asset, or abroad, buying the foreign productiveasset. Without capital mobility, agents can buy only the productive assetlocated at home.3

Agents also receive income in the form of an idiosyncratic stochasticendowment, , that follows a discrete Markov process. Therefore, therewt

are two types of risk due to endowment and investment shocks. We caninterpret as labor income and as capital income.w yt t

The impact of endowment shocks is beyond the control of individualagents, whereas that of investment shocks can be avoided by choosingnot to purchase the productive asset. With this difference at play, wecan distinguish risky from riskless investments so that agents face anontrivial portfolio choice. We can then study not only how financialmarket heterogeneity affects net foreign asset positions but also theircomposition.

3 The limited supply of the productive asset is similar to Lucas’s tree model with twoimportant differences. First, the tree or the fruits of the tree are combined with anotherinput of production, the managerial capital. This introduces decreasing returns to scale.Second, shocks to production, which can also be interpreted as shocks to the fruits of thetree, are project-specific and therefore “idiosyncratic.” In the typical Lucas’s tree model,the realizations of the shocks are the same for all agents operating in the same country;i.e., there are only “aggregate” shocks.




Note that production is individually run and shocks are idiosyncratic:there are no aggregate shocks. Therefore, cross-country sharing of ag-gregate risks is not an issue here. Also notice that there is no aggregateaccumulation of capital. For an extension with capital accumulation,see Mendoza, Quadrini, and Rıos-Rull (2008).

Let be the pair of endowment and investment shocks withs { (w , z )t t t

a Markov transition process denoted by . Agents can buy con-g(s , s )t t�1

tingent claims, , that depend on the next period’s realizations ofb(s )t�1

these shocks. Because there is no aggregate uncertainty, the price ofone unit of consumption goods contingent on the realization of isst�1

, where is the equilibrium interest rate.i i iq (s , s ) p g(s , s )/(1 � r ) rt t t�1 t t�1 t t

Define as the end-of-period net worth before consumption. Theat

budget constraint for an individual agent isi ia p c � k P � b(s )q (s , s ), (1)�t t t t t�1 t t t�1

st�1

and the agent’s net worth evolves according toi na(s ) p w � k P � z k � b(s ). (2)t�1 t�1 t t�1 t�1 t t�1

If asset markets were complete, that is, without restrictions on the setof feasible claims, agents would be able to perfectly insure against allrisks. However, there are market frictions, and the set of feasible claimsis constrained in each country. In particular, we assume that contractsare not perfectly enforceable because of the limited (legal) verifiabilityof shocks. Because of the limited verifiability, agents can divert part oftheir incomes from endowment and production, but they lose a fraction

of the diverted income. The parameter characterizes the degreei if f

of enforcement of financial contracts in country i. This is the onlyfeature that differentiates the two countries.

We also assume that there is limited liability and agents cannot beexcluded from the market after defaulting. Under these assumptions,Appendix B shows that contract enforceability imposes the followingtwo constraints:

i n na(s ) � a(s ) ≥ (1 � f ) 7 [(w � z k ) � (w � z k )] (3)n 1 n n t 1 1 t

and

a(s ) ≥ 0 (4)n

for all . Here n is the index for a particular realizationn � {1, … , N }of the two shocks with the lowest (worst) realization. The number ofs1

all possible realizations is N.The first condition requires that the variation in net worth, a(s ) �n

, cannot be smaller than the variation in income, scaled bya(s ) 1 �1

. This constraint can also be written in terms of the contingent claims.if




From the definition of provided in (2), the constraint (3) cana(s )t�1

be rewritten asi n nb(s ) � b(s ) ≥ �f 7 [(w � z k ) � (w � z k )]. (5)n 1 n n t 1 1 t

When is positive, agents can choose unequal amounts of contingentif

claims, and therefore, they can get some insurance. If is sufficientlyif

large, agents can achieve full insurance. When —implying thatif p 0income can be diverted without losses—only non-state-contingent claimsare feasible. Constraint (4) imposes that net worth cannot be negative.This follows from the assumption of limited liability.

A key assumption is that pertains to the country of residence ofif

the agents, regardless of the geographic location of their assets. In par-ticular, if asset markets are globally integrated, domestic agents can buyforeign productive assets and receive foreign income, but still theiraccess to insurance is determined by the domestic, not the foreign, f.This implies that the ability of an agent to divert investment incomesgenerated abroad depends on the legal environment of the country ofresidence.

This assumption is based on the idea that the verification of diversionrequires the verification of individual consumption. Because individualconsumption takes place in the country of residence, the institutionalfeatures of the country of residence are the ones that matter for en-forcement.4 Section V explores the extent to which our results are robustto alternative assumptions about the residence or source nature of .if

A. Optimization Problem and Equilibrium

Let be a (deterministic) sequence of prices in countryi i �{P , q (s , s )}t t t t�1 tpt

i. With capital mobility these prices are equalized internationally, andtherefore, an individual agent is indifferent about the domestic versusforeign location of the productive investment. We can then write theoptimization problem of an individual agent as if he or she buys onlydomestic k. Independently of the international capital mobility regime,this can be written as

i i ′ ′ ′V (s, a) p max U(c) � b V (s , a(s ))g(s, s ) (6)�t t�1{ }′′ sc,k,b(s )

subject to (1), (2), (3), and (4), where we denote current “individual”variables without subscripts and next period individual variables withthe prime superscript. Notice that this is the optimization problem for

4 One way to think about this assumption is that agents have the ability to repatriatethe incomes earned abroad. Once the incomes are transferred back to the home country,the verifiability of these incomes is determined by the institutions at home.




any deterministic sequence of prices, not only steady states. This mo-tivates the time subscript in the value function.

The solution to the agent’s problem yields decision rules for con-sumption, , productive assets, , and contingent claims,i ic (s, a) k (s, a)t t

. Since in the equilibrium with capital mobility agents arei ′b (s, a, s )t

indifferent about the location of the productive investment, we do nothave to specify whether the holding of productive capital, , isik (s, a)t

domestic or foreign. The decision rules determine the evolution of thedistribution of agents over s, k, and b, which we denote by .iM (s, k, b)t

Definition 1 (Financial autarky). Given the financial developmentindicator, , and initial wealth distributions, , for ,i if M (s, k, b) i � {1, 2}t

an equilibrium without international mobility of capital is defined bysequences of (a) agents’ policies , (b) valuei i i ′ �{c (s, a), k (s, a), b (s, a, s )}t t t tpt

functions , (c) prices , and (d) distributionsi � i i i ′ �{V (s, a)} {P , r , q (s, s )}t tpt t t t tpt

such that (i) the policy rules solve problem (6) andi �{M (s, k, b)}t tpt�1

are the associated value functions; (ii) prices satisfyi � i{V (s, k)} q pt tpt t

; (iii) asset markets clear,′ ig(s, s )/(1 � r )t

i ik (s, a)M (s, k, b) p 1,� t t

s,k,b

i ′ i ′b (s, a, s )M (s, k, b)g(s, s ) p 0� t t′s,k,b,s

for each and ; and (iv) the sequence of distributions isi � {1, 2} t ≥ tconsistent with the initial distributions, the individual policies, and thestochastic processes for the idiosyncratic shocks.

The definition of the equilibrium with globally integrated capital mar-kets is similar, except for the prices and market-clearing conditions iiand iii. With financial integration there is a global market for assets andasset prices are equalized across countries. Therefore, condition iibecomes

′ ′g(s, s ) g(s, s )1 2q p p p qt t1 21 � r 1 � rt t

and . Furthermore, asset markets clear globally instead of coun-1 2P p Pt t

try by country. Therefore, the market-clearing condition for the pro-ductive assets becomes

2

i ik (s, a)M (s, k, b) p 2�� t tip1 s,k,b




and the market-clearing condition for contingent claims becomes

2

i ′ i ′b (s, a, s )M (s, k, b)g(s, s ) p 0.�� t t′ip1 s,k,b,s

With capital mobility, the assets owned by a country are no longerequal to the assets located in the country, and hence NFA positions aregenerally different from zero. Consequently, since at equilibrium agentsare indifferent about the location of the productive investment, onlythe “net” share of the foreign productive asset is determined. The sameholds for the contingent claims. Therefore, the net foreign asset positionof country i is given by

i i ′ ′ iNFA p b (s, a, s )g(s, s )M (s, k, b)t � t t′s,k,b,s

i i� [k (s, a) � 1]P M (s, k, b).� t t t

s,k,b

The first term on the right-hand side is the net position in “contingentclaims.” The second is the net position in “productive assets.” We referto the first term as bond position or international lending when positiveand debt position or borrowing when negative.

B. Equilibria with and without Capital Mobility

This subsection characterizes the properties of the equilibrium with andwithout financial integration. To clarify the different roles played byendowment and investment shocks, we consider separately the caseswith only endowment risks and with only investment risks.

1. Endowment Shocks Only

Assume that z is not stochastic ( ), so that there are only endowment¯z p zshocks. Denote by a sufficiently high value of the enforcement pa-f

rameter so that (3) is not binding and hence markets are complete.With i.i.d. shocks, suffices, whereas persistent shocks requiref p 1

. To show the importance of domestic financial development, wef 1 1compare the limiting cases of complete markets ( ) with the en-¯f p f

vironment without state-contingent claims ( ). We first look at thef p 0autarky regime and then at the financially integrated regime.




When , constraint (3) is not binding by assumption. Therefore,¯f p f

the first-order conditions of problem (6) with respect to k and are′b(w )

′ ′ ′ ′ ′U (c) p b(1 � r )U (c(w )) � (1 � r )l(w ) Gw (7)t t

and

′ ′ ′ ′¯ ¯U (c) p bR (k, z)EU (c(w )) � R (k, z)El(w ), (8)t�1 t�1

where is the Lagrange multiplier associated with the limited lia-′l(w )bility constraint (4), and is the gross mar-n�1¯ ¯R (k, z) p (P � nzk )/Pt�1 t�1 t

ginal return from the productive asset. Notice that is decreas-¯R (k, z)t�1

ing in k.Since in this case agents have complete insurance, condition (7) holds

for any realization of , which implies that next period consumption′wis the same for all . Moreover, conditions (7) and (8) imply′ ′c(w ) w

, so the marginal return on the productive asset is¯R (k, z) p 1 � rt�1 t

equal to the interest rate. Because is strictly decreasing in k,¯R (k, z)t�1

this implies that all agents choose the same input of the productiveasset, that is, . Given that the supply of the productive asset isk p 1fixed, total output is also fixed. We now establish that the full insuranceautarky equilibrium must satisfy .b(1 � r ) p 1t

Lemma 1. Under the financial autarky regime and , the in-¯f p f

terest rate and the price of the productive asset are constant and equalto and , respectively.¯r p 1/b � 1 P p nz/r

Proof. By way of contradiction, if , condition (7) impliesb(1 � r ) ( 1t

that consumption growth of all agents is either positive or negative. Thiscannot be an equilibrium because aggregate output remains constant.Therefore, . Because all agents use the same units ofr p 1/b � 1 p rt

the productive asset, , conditions (7) and (8) implyk p 1 (P �t�1

. The only stationary solution for this difference equation¯nz)/P p 1 � rt

is . QED¯P p P p nz/rt t�1

Consider next the case of an economy in financial autarky but with. The enforceability constraint (3) imposes that …f p 0 b(w ) p p1

; that is, assets cannot be state-contingent. The first-order con-b(w ) p bN

ditions are

′ ′ ′ ′U (c) p b(1 � r )EU (c(w )) � (1 � r )El(w ) (9)t t

and

′ ′ ′ ′¯ ¯U (c) p bR (k, z)EU (c(w )) � R (k, z)El(w ). (10)t�1 t�1

These conditions still imply that , and the input of¯R (k, z) p 1 � rt�1 t

the productive asset is the same for all agents. Thus, all agents receivethe same investment income. However, the absence of state-contingent




assets implies that the endowment risk cannot be insured and individualconsumption is not constant. It varies with the realization of the en-dowment as in the standard Bewley (1986) economy. As is known fromthe savings literature (see Huggett 1993; Aiyagari 1994; Carroll 1997),the uninsurability of the idiosyncratic risk generates precautionary sav-ings and in the steady state . Formally, we have the followingb(1 � r) ! 1lemma.

Lemma 2. Under the financial autarky regime and , the in-f p 0terest rate satisfies and the steady-state price is .¯r ! 1/b � 1 P p nz/rt

The proof is standard and uses convexity of marginal utility togetherwith the fact that all households employ the same amount of productiveasset.

Using these lemmas, we can compare countries in financial autarkyat different stages of financial development: The country with a lowerdegree of financial development ( ) has a lower interest rate and,f p 0at least in the steady state, a higher asset price than a more financiallydeveloped country.

Consider now the steady-state equilibrium of an economy in whichthere is perfect mobility of capital between country 1 (henceforth C1),characterized by , and country 2 (henceforth C2), characterized1 ¯f p f

by . In this case, the perfect substitutability of assets implies that2f p 0their prices are equated across countries, and so are the world interestrate and the holdings of productive assets by all agents. Given that C1has no need for precautionary savings but C2 does, the conflict getsresolved by households in C1 hitting the limited liability constraint (4).The following proposition formalizes this result.

Proposition 1. Suppose that and . In the equilib-1 2¯f p f f p 0rium with financial integration, , and C1 accumulates a neg-r ! 1/b � 1t

ative NFA position but holds a zero net position in the productive asset.Proof. See Appendix C.This proposition holds only for the limiting cases of and1 ¯f p f

. However, we can infer the properties of the equilibrium for2f p 0intermediate values of f (i.e., for any case ). In general,2 1 ¯0 ≤ f ! f ! f

lower values of f increase precautionary savings and reduce the equi-librium interest rate. Therefore, once the capital markets are liberalized,the country with a lower value of f accumulates a positive NFA position.

This point is illustrated in figure 4. The figure plots the aggregatedemand for assets (supply of savings) in each country as an increasingfunction of r.5 Country 1 has deeper financial markets ( ) and1 2f 1 f

5 The asset demand curves in fig. 4 correspond to the well-known average asset demandcurve from the closed-economy heterogeneous agents literature (e.g., Aiyagari 1994).Average asset demand approaches infinity as the interest rate converges to the rate oftime preference from below. The reason is that agents need an infinite amount of pre-cautionary savings to attain a level of consumption that is not stochastic.




Fig. 4.—Steady-state equilibria with heterogeneous financial conditions: A, autarky; B,mobility.

hence lower asset demand for each interest rate. Because the supply ofthe productive asset is fixed, aggregate net savings (in units of K) mustbe zero under autarky in each country. This requires a higher interestrate in C1 ( ).1 2r 1 r

2. Investment Shocks Only

We now consider the case in which the productivity z is stochasticwhereas the endowment is constant at . This assumption allows¯w p wus to distinguish debt instruments from risky investments such as FDI.As before, we compare equilibria under autarky and under financialintegration for the limiting cases of and .¯f p f f p 0

The first-order conditions in autarky for an economy with are¯f p f

′ ′ ′ ′ ′U (c) p b(1 � r )U (c(z )) � (1 � r )l(z ) Gz (11)t t

and

′ ′ ′ ′ ′ ′U (c) p bER (k, z )U (c(z )) � El(z )R (k, z ). (12)t�1 t�1

The first condition holds for all realizations of . Therefore, the next′zperiod’s consumption, , must be the same for all realizations of′ ′c(z ) z(full insurance). Because next period’s consumption is not stochastic,conditions (11) and (12) imply that . Therefore,′ER (k, z ) p 1 � rt�1 t

there is no marginal premium for investing in the productive asset andk is the same for all agents. Thus, lemma 1 also applies here and theonly equilibrium is characterized by . Intuitively, becauseb(1 � r ) p 1t

agents can insure perfectly against the idiosyncratic risk, there are noprecautionary savings and in equilibrium the interest rate must be equalto the intertemporal discount rate.

In an economy with , the incentive-compatibility constraint (3)f p 0




imposes that ; that is, claims cannot be state con-…b(z ) p p b(z ) p b1 N

tingent. The first-order conditions are

′ ′ ′ ′U (c) p b(1 � r )E[U (c(z ))] � (1 � r )E[l(z )] (13)t t

and

′ ′ ′ ′ ′ ′U (c) p bE[U (c(z ))R (k, z )] � E[l(z )R (k, z )]. (14)t�1 t�1

Lemma 2 also applies here; hence, the equilibrium interest rate issmaller than the intertemporal discount rate. The main difference withthe case of endowment shocks is that now there is a marginal risk pre-mium for the risky asset. In particular, if the borrowing limit is notbinding, conditions (13) and (14) yield the standard equation for therisk premium:

′ ′ ′Cov [R (k, z ), U (c(z ))]t�1′ER (k, z ) � (1 � r ) p � ,t�1 t ′ ′EU (c(z ))

which is positive as long as is negatively correlated with′ ′U (c(z )).′R (k, z )t�1

Now suppose that the two countries become financially integrated.The first country has and the second . The following1 2¯f p f f p 0proposition characterizes the steady state.

Proposition 2. Suppose that and . In the steady1 2¯f p f f p 0state with financial integration, . Country 1 has a negativer ! 1/b � 1NFA position but a positive position in the productive asset. The averagereturn of C1’s foreign assets is larger than the cost of its liabilities.

Proof. See Appendix C.The proposition shows that, with investment shocks, countries with

deeper financial markets invest in foreign (high-return) assets and fi-nance this investment with foreign debt. In the particular case in whichthe most developed country has , proposition 1 guarantees that1 ¯f p f

this country ends up with a negative NFA position. The higher returnderives from the decreasing returns property of the production function.This generates a surplus that compensates the agent’s managerialcapital.

Consider now the general case with . Country 1 has a2 1 ¯0 ≤ f ! f ! f

greater (yet imperfect) ability to insure than C2, and hence it will stillbuy some of C2’s risky asset,6 even if it is not always true that it accu-mulates a negative NFA position. Moreover, the imperfect insurancegenerates a marginal risk premium even for C1, which is the rationale

6 The concavity of the production function is crucial for this result. With a linear tech-nology, as in Angeletos (2007), the most developed country would own all of the world’srisky assets. As a result, the less developed country would have fewer incentives to save.




for the higher return that C1 collects from its foreign investments rel-ative to the cost of its foreign liabilities.

3. Endowment and Investment Shocks

With both endowment and investment shocks, the first-order conditionsare also given by (11)–(14). The only difference is that next period’sconsumption depends on both shocks, that is, . The autarky equi-′c(s )libria are also characterized by lemmas 1 and 2. The following propo-sition characterizes the equilibrium under global financial integration.

Proposition 3. Suppose that and . In the steady1 2¯f p f f p 0state with perfect capital mobility, . Country 1 has a negativer ! 1/b � 1NFA position but a positive position in foreign productive assets. Theaverage return of C1’s foreign ownership is bigger than the cost of itsliabilities.

Proof. Same as in proposition 2.This is a restatement of proposition 2 for the case with both shocks.

In the extreme case with and , the addition of endowment1 2¯f p f f p 0shocks does not change the main properties of the equilibrium. In thegeneral case, the interest rate is smaller than the intertemporal discountrate, and C1 acquires a positive net position in foreign productive assets,but its NFA position is not necessarily negative. This depends on therelative importance of the two shocks. As long as the endowment shockis sufficiently large, however, C1 will hold a negative NFA position.

III. The General Model

We now extend the basic setup presented in the previous section alongtwo dimensions: (1) cross-country diversification of the investment riskand (2) differences in the economic size of countries. We also generalizethe model to include any finite number of countries . These fea-I ≥ 2tures allow for a richer quantitative analysis.

We introduce international risk diversification by assuming that man-agerial capital is now divisible across countries. Each agent is endowedwith one unit of this capital. With denoting the allocationA � [0, 1]j,t

of an agent’s managerial capital in country j, the total (worldwide)production at time of the agent is equal tot � 1

I I

1�n ny p z A k , with A p 1.� �t�1 j,t�1 j,t j,t j,tjp1 jp1

The variables and are, respectively, the project-specific idiosyn-z kj,t�1 j,t

cratic shock and the input of the productive asset in country j.The divisibility of the managerial capital is the most important ex-




tension. In the basic model, each agent had to choose allocating all themanagerial capital either in C1 ( and ) or in C2A p 1 A p 01,t 2,t

( and ). In contrast, now agents can allocate any fractionA p 0 A p 11,t 2,t

in each of the I countries. This has two important impli-A � [0, 1]j,t

cations. First, as long as the shocks are imperfectly correlated,z j,t�1

financial integration allows agents to diversify investment risk acrosscountries.7 Second, while in the basic model only the net foreign po-sition in the productive asset was determined at equilibrium, now thegross positions are also determined.

Let be the endowment and investment shockss { (w , z , … , z )t t 1,t I,t

and their transition probabilities. As in the basic model, agentsg(s , s )t t�1

can buy contingent claims, . The price of one unit of consumptionb(s )t�1

goods contingent on the realization of is is q (s , s ) p g(s ,t�1 t t t�1 t

, where is the equilibrium interest rate in country i.i is )/(1 � r ) rt�1 t t

Given the end-of-period net worth before consumption, , the budgetat

constraint is

I

j ia p c � k P � b(s )q (s , s ), (15)� �t t j,t t t�1 t t t�1jp1 st�1

and net worth evolves according to

I

j 1�n na(s ) p w � (k P � z A k ) � b(s ). (16)�t�1 t�1 j,t t�1 j,t�1 j,t j,t t�1jp1

The features of the financial environment are the same as in the basicmodel: shocks are not verifiable and agents can divert part of the in-comes from endowment and production, both domestic and abroad,but in the process they lose a fraction of the diverted income. Asif

before, pertains to the residence of agents as opposed to the sourceif

of the income.Following the same steps of Appendix B, the enforcement of financial

contracts imposes the following constraints:

I

i 1�n na(s ) � a(s ) ≥ (1 � f ) 7 w � w � (z � z )A k (17)�n 1 n 1 j,n j,1 j,t j,t[ ]jp1

and

a(s ) ≥ 0 (18)n

for all , where N is the number of all possible realizationsn � {1, … , N }

7 We are implicitly assuming that agents do not benefit from allocating their managerialcapital to multiple operations within each country. The only diversification gains arisefrom cross-country diversification. Without loss of generality, we can interpret as thezj,t�1

residual risk after exploiting all the diversification margins available within each country.




of endowment and investment shocks and is the lowest (worst) re-s1

alization.8

There is a difference with the previous constraint (3). Now individualagents have both differentiated domestic and foreign incomes fromproductive investments. Before, all income from productive investmentswas subject to the same shock and hence could not be distinguished.

The last extension of the model relates to the economic size of coun-tries participating in world capital markets. This is important for thequantitative properties of the model. Obviously, large imbalances forC1 can arise only if the economy of C2 is relatively large. In our model,differences in economic size could derive from differences in populationand/or in productivity, that is, in the average value of the endowmentw and in the per capita supply of the productive asset k. However, forthe properties we are interested in, what matters is differences in theaggregate economic size of countries, independently of the factors thataccount for them. Therefore, to simplify the analysis, we assume thatdifferences in economic size derive only from differences in population.

We denote by the population share of country i and continue toim

assume that the per capita endowment w and the per capita domesticsupply of the productive asset are the same in all countries. This ex-tension does not alter the analytical results of Section II.

Optimization problem and equilibrium.—Given deterministic sequencesof prices , a single agent’s problem in country i canj j � I{{P , q (s , s )} }t t t t�1 tpt jp1

be written as

i i ′ ′ ′V (s, a) p max U(c) � b V (s , a(s ))g(s, s ) (19)�t t�1{ }′′ sA,k,b(s )

subject to (15), (16), (17), (18), and

I

A � [0, 1], A p 1.�j jjp1

The definition of the autarky equilibrium is equivalent to the defi-nition provided for the basic model. The reason is that all the extensionsintroduced in this section matter only for the regime with capital mo-bility. With capital mobility the individual state variables are given by(s, A, k, b). The variable s is an –dimensional vector containing theI � 1realization of the endowment plus the realizations of the investmentshocks in each of the I countries. The variables A and k, without sub-scripts, are I-dimensional vectors containing, respectively, the allocationof managerial capital and the ownership of productive assets in each of

8 A generic contains elements: the endowment shock and the realizations ofs 1 � I wn n

the idiosyncratic shocks in each of the I countries, i.e., for .z j p 1, … , Ij,n




the I countries. Finally, the realized claim b remains one-dimensionalas in the simpler version of the model. The definition of the equilibriumwith capital mobility is as follows.

Definition 2 (Financial integration equilibrium). Given the finan-cial development indicator, , and initial wealth distributions,i if M (s,t

, a general equilibrium with international capital mobility isA, k, b)defined by sequences of (a) individual policies

i i ′ i i I �{c (s, a), b (s, a, s ), {A (s, a), k (s, a)} } ,t t j,t j,t jp1 tpt

(b) value functions , (c) prices , and (d)i � j j j ′ I �{V (s, a)} {{P , r , q (s, s )} }t tpt t t t jp1 tpt

distributions such that (i) the policy rules solve prob-i �{M (s, A, k, b)}t tpt�1

lem (19) with as associated value functions; (ii) prices satisfyi �{V (s, a)}t tpt

; (iii) the global markets for the productive assets of eachj ′jq p g(s, s )t t

country clear,

I

i i jk (s, a)M (s, A, k, b) p m�� j,t tip1 s,A,k,b

for ; (iv) the worldwide market for contingent claims clears,j p 1, … , I

I

i ′ i ′b (s, a, s )M (s, A, k, b)g(s, s ) p 0;�� t t′ip1 s,A,k,b,s

and (v) the sequence of distributions is consistent with the initial dis-tributions, the individual policies, and the idiosyncratic shocks.

It is important to emphasize that, in general, the market-clearingconditions for productive assets do not lead to the equalization of theirprices; that is, is not equal to for . The reason is that unlessi jP P i ( jt t

the shocks are perfectly correlated across countries, agents are not in-different about the composition of their portfolios of productive assets.This is in contrast to the equalization of the interest rates: all that mattersfor the choice of the contingent claims is their returns, which are de-termined by the interest rate.

It is possible to derive some analytical results for this general modelthat are similar to those of the basic model. The optimality conditionsare analogous, except that now we also have the conditions character-izing the optimal cross-country allocation of managerial capital. Theseconditions are for all . If we consider the casek /A p k /A j p 1, … , Ii i j j

in which , , and , we can prove that the same prop-1 2¯I p 2 f p f f p 0erties shown in Section II.B apply to the general model. This is obviousbecause, with , agents in C1 do not require a marginal premium1 ¯f p f

on the productive investments. Hence, they are indifferent about thedomestic and foreign allocation of the managerial capital.




IV. Quantitative Analysis

We now turn to the quantitative implications of the model. The goal isto compare stationary equilibria under financial autarky and perfectcapital mobility and to study the transitional dynamics from the formerto the latter. Financial globalization is introduced as a once-and-for-allunanticipated regime change. We use a baseline scenario with .I p 2The first country, C1, is representative of the United States. The secondcountry, C2, aggregates all remaining countries. Later on we add a thirdcountry to separate emerging economies from industrial countries otherthan the United States.

A. Calibration

We set the population size of C1 to so as to match the U.S.1m p 0.3share of world GDP, which is about 30 percent. The stochastic endow-ment takes two values given by , with a symmetric tran-¯w p w(1 � D )w

sition probability matrix. The investment shock also takes two values,, but it is assumed to be i.i.d. Interpreting w as labor¯z p z(1 � D )z

income and y as net capital income, we set , and then wew p 0.85parameterize the production function so that . Becausen¯y p zk p 0.15per capita assets are , this requires . The share of labor¯k p 1 z p 0.15is higher than the typical value of two-thirds because it is in terms ofnet income, that is, income net of depreciation. The return to scaleparameter is set to , implying a share of managerial capital ofn p 0.750.25. This generates managerial rents as a fraction of total net incomethat are relatively small, about 3.75 percent.9

For the calibration of the stochastic process of the endowment, wefollow recent estimates of the U.S. earnings process and set the persis-tence probability to 0.95 and . These values imply that logD p 0.6w

earnings have an autocorrelation coefficient of 0.9 and a standard de-viation of 0.30, which are in the ranges of values estimated by Stores-letten, Telmer, and Yaron (2004). The variation in the investment shockis set to . This implies that the return on productive assetsD p 2.5z

fluctuates between �6 percent and 14 percent. We take this as an ap-proximation to the volatility of firm-level returns. The correlation inproductivity shocks across the different projects is set to zero. Therefore,there is wide scope for international diversification of investment risks.

Next we choose the parameters of the financial structure. Several

9 Because the capital income generated by productive activities is 15 percent of totalnet income and the rents are about 25 percent of capital income, the share of rents intotal net income is about . This is close to Rotemberg and Woodford’s0.15 # 0.25 p 0.0375(1995) 3 percent estimate of the profit rate in U.S. firm-level data, although the twoestimates are not directly comparable.




indicators, such as those reported in figure 1, suggest that financialmarkets are significantly different across countries. However, it is dif-ficult to derive a direct mapping from these indicators to the actualvalues of . Given these difficulties, we take a pragmatic approach. Weif

begin by assigning some values and then we conduct a sensitivity analysis.We start with and . Thus, contingent claims are partially1 2f p 0.35 f p 0available in C1 and unavailable in C2. It is also worth observing thatthere is a certain degree of equivalence between cross-country differ-ences in f’s and differences in the volatility of idiosyncratic shocks. Theassumption that implies that the equilibrium allocation in C11f p 0.35is similar to the one that would prevail if contingent claims were notavailable (i.e., ) but the volatilities of all shocks were 35 percent1f p 0lower than in C2.

The utility function is constant relative risk aversion (CRRA), withthe coefficient of risk aversion set to . The intertemporal discountj p 2factor is . With this discount factor, the wealth-to-income ratiosb p 0.925in the steady state with capital mobility are 2.86 in C1 and 3.45 in C2.The worldwide wealth-to-income ratio is about 3.3. This is higher thanthe typical number of 3 because our income is net of depreciation. Thedescription of the computational procedure is provided in AppendixD.

B. Results

Individual policies.—Figure 5 plots the individual decision rules as afunction of the net worth a, for each value of the endowment w, in thesteady state with capital mobility.10 Three variables are plotted: the valueof all contingent claims, ; the value of productive assets′ ′� b(s )q(s, s )′s

purchased in C1, ; and the value of productive assets purchased ink P1 1

C2, .k P2 2

The net position in contingent claims increases with net worth: it isnegative for poorer agents and positive for richer agents. The totalposition in risky investments also increases with a. For the range of aplotted in the figure, all agents choose to buy productive assets in bothcountries. However, as agents become wealthier, they allocate a largerproportion in C2.

The intuition for this pattern can be described as follows. First, weshould observe that, because of the different economic size of the twocountries, the equilibrium price of the productive asset in C2 is smallerthan in C1. Suppose on the contrary that the two prices were the same.

10 The current realization of the endowment is a state variable because endowmentshocks are persistent. The investment shock z can be ignored as a state variable becauseit is i.i.d.




Fig. 5.—Policy rules as functions of net worth

Because investment shocks are uncorrelated across the different proj-ects, when the prices of the productive assets are the same, investorswould allocate an equal share of their investments between the domesticand the foreign projects. Therefore, the total demand for the productiveasset in C1 would be exactly equal to the total demand for the productiveasset in C2. However, because C2 is larger than C1, the supply in C1 issmaller than in C2. This generates a decline in the price of the pro-ductive asset in C2 relative to the price in C1. The lower price of theproductive asset in C2 implies that the expected return from investingin C2 is higher than in C1. Given CRRA utility, as agents become wealth-ier, they assign higher weight on returns and less on risk. Therefore,they value less the benefits from diversification and invest more in C2.

Aggregate variables.—Panel A of table 1 reports the equilibrium pricesand positions that prevail in the steady-state equilibria under autarkyand perfect capital mobility. Under capital mobility, C1 accumulates anet positive position in productive assets but a much larger negativeposition in contingent claims (bonds).

Country 1’s debt and foreign risky asset positions are �89 and 37percent of its domestic income, respectively. As a result, the NFA position




TABLE 1Steady State with and without Capital Mobility

Autarky Capital Mobility

C1 C2 C1 C2

A. Both Shocks

Prices of productive assets 3.08 3.40 3.38 3.22Returns on productive assets 4.80 4.30 4.41 4.58Standard deviation of returns 8.11 11.76 8.83 8.95Interest rate 3.25 2.60 3.05 3.05Net foreign asset positions . . . . . . �51.39 22.12

Productive assets . . . . . . 37.41 �16.10Bonds . . . . . . �88.80 38.22

Welfare gains from liberalization 2.63 �.27

B. Endowment Shocks Only

Prices of productive assets 2.95 3.22 3.14 3.14Returns on productive assets 5.08 4.66 4.78 4.78Standard deviation of returns .00 .00 .00 .00Interest rate 3.81 3.49 3.58 3.58Net foreign asset positions . . . . . . �38.69 16.58

Productive assets . . . . . . .00 .00Bonds . . . . . . �38.69 16.58


C. Investment Shocks Only



Welfare gains from liberalization .60 .20

Note.—Foreign asset positions are in percentage of domestic income (endowment plus domestic investment income).Welfare gains are in percentage of consumption.

is negative and quite large, �51 percent of income. Hence, the modelis consistent with the data in predicting that the most financially de-veloped country accumulates a substantial negative NFA, chooses a risk-ier portfolio, and experiences a reduction in the risk-free rate relativeto autarky. However, the model overstates the adjustment observed sofar in the U.S. economy. As of 2004, the net positions in debt and riskyassets were �32 and 9 percent of U.S. GDP, respectively, and the totalNFA position was �24 percent of GDP. Note also that the changes inasset prices and interest rates that support these large changes in assetholdings are small.

The model also predicts that financial globalization leads to an in-crease in the gross holdings of foreign risky assets for all countries (seefig. 5). As Lane and Milesi-Ferretti (2007) noted, this is a salient featureof the financial globalization era (see fig. 2B).




A feature of the equilibrium is that the average return from the pro-ductive assets is greater than the interest rate. This derives from twomechanisms. First, because of decreasing returns, there is a surplus thatcompensates managerial capital. Therefore, even if the marginal returnon the productive asset is equal to the interest rate, total production isbigger than the opportunity cost of the investment.11 The second mech-anism relates to the investment risk. Because of this risk, investors re-quire a marginal premium over the interest rate that further increasesthe average return.

Consider now the special versions of the model with only endowmentor investment shocks. Panels B and C of table 1 report the steady-statevalues of some key variables in these cases. With endowment shocks only(panel B), the model can produce a large negative NFA position in C1(of roughly �38 percent of domestic income). However, with only en-dowment shocks, the model cannot explain the observed shift in thecomposition of the portfolios of foreign assets. By contrast, the setupwith only investment shocks (panel C) does produce a portfolio for C1characterized by a negative debt position and a positive position in riskyassets. The total NFA position, however, is not very large. The reason isthat as C1 takes a greater position in risky assets, it faces greater riskinducing higher savings.

In summary, these results show that by combining endowment andinvestment shocks, we can capture both features of the U.S. internationalasset position: large net foreign liabilities and a portfolio compositiontilted toward high-return assets.

Transition after liberalization.—Figure 6 plots the transitional dynamicsfrom autarky to full financial integration for several aggregate variables.The top left panel shows that the decline in net foreign assets in C1 isa slow, gradual process that takes about 30 years. The current accountdrops to a deficit of almost 4 percent of domestic income on impactand remains in deficit for many periods until it converges to zero inabout 50 years.

The deterioration of the current account in C1 is not as gradual asin the U.S. data. In our results, however, the pattern of a large initialdeficit followed by gradual recovery is a consequence of the assumptionthat capital markets are fully integrated overnight. In reality, financialintegration has been a gradual process (see fig. 2). With gradual inte-gration the model would have displayed current account dynamics morein line with the U.S. data.

Figure 6 also plots the dynamics for the components of NFA and thecurrent account. Immediately after financial integration, C1 purchases

11 Decreasing returns are important for this feature of the model and for supporting awell-defined portfolio choice.




Fig. 6.—Transition dynamics after capital markets liberalization

a large quantity of foreign productive assets financed with foreign debt.Despite the negative NFA position, C1 receives initially positive net factorpayments from abroad as a result of the higher return on the productiveassets. These payments, however, are more than compensated by neg-ative net exports, and thus the country experiences current accountdeficits until it reaches the new steady state.




Fig. 7.—Welfare effects of financial integration

Normative implications.—We examine next the normative implicationsof the model. We are interested in answering two questions. First, isfinancial integration welfare enhancing for the participating countries?Second, how are the welfare effects distributed among the populationof each country?

The model features three mechanisms by which financial integrationcan affect welfare. First, by investing in both countries, households candiversify the investment risks. Second, countries can specialize in more(C1) or less (C2) risky activities. Third, financial integration can benefitC1 citizens and hurt C2 residents because its effects on asset prices causecapital gains and losses and changes in the rate of interest (see fig. 6).

Figure 7 plots the welfare gains (or losses if negative) from financialintegration as a function of individual net worth, a, and endowment,w, when the reform is introduced. These welfare gains are computedas the percentage increase in consumption in the autarky steady statethat makes each individual agent indifferent between remaining in au-tarky and shifting to the regime with financial integration. The figurealso shows, for each country, the distribution of agents over net worthin the autarky steady state. This is the initial distribution when theinternational capital markets are liberalized.

In C1 all agents gain from liberalization, and the gains are especially




large for agents with lower initial wealth. For these agents, the gainsderive from all the reasons described above, and in particular from thereduction in the interest rate. As shown in the bottom-left chart of figure7, poorer agents are initially net borrowers, and therefore, they benefitfrom a reduction in the interest rate. Richer agents, instead, are netlenders, and they are hurt by lower interest rates.

The increase in the interest rate relative to autarky in C2 affectsnegatively the welfare of its poorer residents because they are net bor-rowers. These effects are large, and the global effect is a reduction intheir welfare. Richer residents in C2 experience overall an increase inwelfare.

We aggregate the individual welfare effects using a social welfare func-tion that weights each agent’s utility equally. The aggregate welfareeffects are measured by the same percentage increase in the consump-tion of all agents in the autarky steady state that makes the value of theaggregate welfare equal to the value in the regime with financial inte-gration. We find that C1 gains about 2.6 percent of aggregate con-sumption and C2 loses 0.27 percent.

C. Sensitivity to the Cross-Country Correlation of Shocks

Table 2 reports the steady-state statistics under autarky and financialintegration for correlated cross-country investment shocks. Panel A as-sumes a correlation of 0.5, which reduces the gains from internationaldiversification of investment, and in panel B the correlation is one,which completely eliminates such gains.12

While the table shows a reduction in the absolute value of the NFAposition of C1, such a position is still very large. The increase in thecorrelation of shocks also increases the two components of the NFAposition in absolute value, since the gains of specialization are nowlarger.

The ability to diversify the investment risk is important for welfare.As we increase the cross-country correlation of shocks, and hence reducethe ability to diversify the investment risk, the welfare gains from inter-national capital market integration become smaller. As a result, C1’sgain falls and C2’s loss rises.

V. Residence- versus Source-Based Enforcement

The analysis conducted so far was based on the assumption that theenforcement parameter f is residence based (i.e., it depends on the

12 International output correlations are typically in the 0.4–0.7 range, but the relevantcorrelations to match with the model should be measured at the level of individual in-comes, not aggregate output.




TABLE 2Sensitivity to the Cross-Country Correlation of Shocks


C1 C2 C1 C2

A. Shocks Are Partially Correlated (Correla-tion p .5)




B. Shocks Are Perfectly Correlated (Correla-tion p 1)




Note.—See table 1.

country of residence of the agents, independently of whether their in-comes are generated at home or abroad) rather than source based (i.e.,it depends on where the incomes are generated). Such an assumptionis based on the view that the ability to verify diversion requires theverification of individual consumption, which uses the resident’s coun-try’s legal system. We now explore environments with alternative as-sumptions about the residence or source nature of the enforcement ofcontracts. We consider four alternative scenarios, with results reportedin table 3. In all the experiments, we use the same values of f as in thebaseline calibration, that is, and .1 2f p 0.35 f p 0

In panel A the enforcement of contracts for residents of C1 remainsas in the baseline model; that is, f1 applies to both foreign and domesticincomes. Residents of C2 are bound by f2 for incomes earned at homeand by f1 for incomes earned abroad. Therefore, C2 residents use thelegal system of C1 for incomes earned abroad. The enforcement con-straint for C2 becomes

2 n 1 n 1 1�n na(s ) � a(s ) ≥ (1 � f ) 7 [w � w � (z � z )A k ]n 1 2 2 2,t 2,t

1 n 1 1�n n� (1 � f )(z � z )A k . (20)1 1 1,t 1,t

Panel B reverses the situation: C1 residents can use their country’s



TABLE 3Sensitivity to Alternative Assumptions about the Nature of f


C1 C2 C1 C2

A. Source Based Only for Residents of C2




B. Source Based Only for Residents of C1




C. Partially Source Based for Residents ofBoth Countries




D. Source Based for Residents of BothCountries


Productive assets . . . . . . �22.13 9.55Bonds . . . . . . �31.89 13.76






legal system for activities carried out domestically, but they have to usethe legal system of C2 for incomes earned abroad. Residents of C2 usetheir own legal system for all economic activity. Panel C considers thesituation in which the enforcement is in part source based and in partresidence based for the residents of both countries. More specifically,the foreign incomes earned by the residents of both countries are en-forced according to . This implies that agents in C1 get1 2f p (f � f )/2less insurance on foreign earned incomes than on domestic incomesbut still greater than the insurance available to residents of C2. Similarly,C2 agents can get better insurance on incomes earned abroad but notas good as the C1 residents. Finally, panel D considers the case in whichenforcement is fully source based in both countries.

Panels A–C of table 3 show that C1 accumulates a large negative NFAasset position and keeps a positive position in productive assets. There-fore, even with partial residence-based enforcement, C1 continues tohave a positive position in productive assets together with a negativeNFA. In panel D, where enforcement is fully source based, however, thenet position in productive assets becomes negative.

VI. Alternative Forms of Financial Development: Industrializedversus Emerging Economies

The only form of financial heterogeneity considered so far derives fromcross-country differences in the parameter f. In this section we considera second form of financial heterogeneity captured by differences in theliability constraint (condition [4]). This constraint can be written moregenerally as , where is a parameter that differs across coun-i ia(s ) ≥ a an

tries. Hence, financial development is now captured by differences inand .i if aBy adding a third country and characterizing financial heterogeneity

in terms of both and , we can replicate the main features of thea f

composition of foreign assets observed separately for the United States,other industrialized countries, and emerging economies. Before addinga third country, we examine how the properties of the model changewith different f’s and/or ’s in the two-country setup.a

Table 4 compares steady states under autarky and financial integrationfor different combinations of f and . Panel A assumes that both coun-atries have the same f, but C1 is still more financially developed becauseit has a lower value of . Panel B allows C1 to be more financiallyadeveloped in both dimensions, higher f and lower .a

Independently of whether financial heterogeneity derives from dif-ferences in f or , C1 ends up with a large negative NFA position. Thereaare important differences, though, in the composition of NFA. In panelA, where the differences are only in , C1 also has negative net holdingsa




TABLE 4Steady State with Heterogeneity in f and a


C1 C2 C1 C2

A. Differences in Only: , ,1 2a a p �1 a p 01 2f p f p .35


Productive assets . . . . . . �13.96 6.01Bonds . . . . . . �51.85 22.30


B. Differences in Both: , ,1 2a p �1 a p 0,1 2f p .35 f p 0





of the productive assets (because of the lower prices of foreign assets).In panel B, with differences in f, C1 takes a positive net position inproductive assets.

These results indicate that cross-country differences in f are neededin order to generate a situation in which the United States accumulatesa negative NFA position and a positive position in high-return assets.Differences in cannot yield this outcome by themselves because loweravalues of decrease the propensity to save but do not change the pro-apensity to take investment risks.

A. A Three-Country Model

It is reasonable to argue that the United States and other industrialcountries do not differ much in the institutional and technological en-vironment that allows for the insurance of income risks. Yet, the evidencereviewed in the introduction shows that the development of nonbankfinancial intermediation has progressed more in the United States, andthis is also consistent with the higher ratio of domestic credit to theprivate sector to GDP of the United States compared to other indus-




trialized countries.13 This suggests that the differences in financial mar-kets between the United States and other industrialized countries aremore likely to derive from differences in than in f. However, theafinancial market differences between the United States and emergingeconomies, where the ability to insure risks is much weaker and thevolume of credit is much lower, are likely to derive from both and f.a

To capture these ideas, we extend the model to study the implicationsof financial integration among three countries or regions: the UnitedStates (C1), other developed countries (C2), and emerging economies(C3). On the basis of the above discussion, we assume that C1 differsfrom C2 only in whereas it differs from C3 in both f and . We seta a

and .14f p (0.5, 0.5, 0) a p (�1, 0, 0)We capture the differences in the economic size of the three countries

by setting relative population sizes to . As explainedm p (0.3, 0.5, 0.2)earlier, by setting the population share of emerging economies to 0.2,we capture the fact that these economies contribute about 20 percentof the world GDP.

Except for the parameters of the financial structure and relative pop-ulation, all other parameters are as in the baseline parameterization.The key steady-state variables are reported in table 5.

The foreign asset structure of the three countries is broadly consistentwith the asset structure shown in figure 3 for the United States, otherindustrialized countries, and emerging economies. In particular, underfinancial integration the other industrialized countries (C2) have a po-sition in risky assets very similar to that of the United States (C1). How-ever, the NFA position is significantly smaller compared to C1. Yet, C3,which represents the emerging economies, has a positive NFA positionand a negative net position in risky assets. The large increase in net

13 According to the World Bank’s World Development Indicators, in 2004 domestic creditto the private sector was 191 percent of GDP in the United States vs. 136 percent for theother Group of Seven countries and 122 percent for the average of OECD countriesexcluding the United States.

14 While it is difficult to obtain direct evidence about the availability of insurance againstincome risks, there are some studies suggesting that insurance is smaller in emergingeconomies than in developed countries, even if only for regional instead of individualshocks. For example, Xu (2008) finds that there is less consumption risk sharing acrossChinese provinces than across U.S. states and Canadian provinces and concludes that“Chinese households would be willing to pay dearly to insure their consumption againstidiosyncratic shocks” (340). In the same vein, Kim, Kim, and Wang (2006) estimate thedegree of consumption risk sharing among 10 East Asian countries and find that about80 percent of the cross-sectional variation of GDP is not smoothed within the region.Compared to the OECD countries, the degree of risk sharing achieved is significantlylower and the potential gains are larger. An implication of the lower f in emergingeconomies under autarky is that the risk-free interest rate is lower. In this regard, Bailey(1994) reports that in the early stages of China’s financial opening, there were A sharestargeted at Chinese savers and B shares for non-Chinese. Type B shares were sold at alarge discount, indicating that the internal rate of return was much lower for Chinesehouseholds.




TABLE 5Steady State in the Three-Country Economy


C1 C2 C3 C1 C2 C3

Prices of productive assets 2.65 2.95 3.40 2.86 2.84 2.88Returns on productive

assets 5.63 5.05 4.30 5.16 5.17 5.36Standard deviation of

returns 7.17 6.44 11.76 4.20 4.23 8.17Interest rate 3.96 3.53 2.60 3.73 3.73 3.63Net foreign asset positions . . . . . . . . . �72.92 2.88 103.15

Productive assets . . . . . . . . . 9.32 9.51 �38.56Bonds . . . . . . . . . �82.24 �6.63 141.72

Note.—The heterogeneous parameters are , , and . See also tablef p (0.5, 0.5, 0) a p (�1, 0, 0) m p (0.3, .0.5, 0.2)1.

bond holdings suggests that if the foreign bonds are held by officialinstitutions, the model can explain the recent surge in the foreign re-serves of emerging economies.

B. Adding Differences in Growth and Income Volatility

Our model is robust in predicting that, as long as there are differencesin domestic financial markets between industrialized and emergingeconomies, financial globalization may result in the latter becoming netsuppliers of funds to the former. In making this case we abstracted fromtwo other important dimensions in which emerging economies differfrom industrialized countries: growth rates and income volatility.

Growth differences can be important because, as predicted by thestandard neoclassical open-economy model, countries experiencing fast-er growth (emerging economies) should borrow from slow-growingcountries (industrialized economies). However, recent trends seem tosuggest the opposite (see, e.g., Gourinchas and Jeanne 2007).

The prediction of the neoclassical model about the flow of capitalfor fast-growing countries is an unavoidable consequence of CRRA pref-erences. If we ignore uncertainty, the Euler equation reads as

. Faster growth in consumption before financial in-j(c /c ) p b(1 � r )t�1 t t

tegration implies a higher value of the left-hand-side term of the Eulerequation, which in turn implies a higher interest rate. As a result, whencountries experiencing faster than average growth become financiallyintegrated, their interest rates converge to a lower “world” interest rateand save less.

If we abstract from heterogeneity in domestic financial markets, ourmodel shares the same features of the neoclassical model. However,once we introduce financial market differences, we have two opposing




effects. The higher growth of emerging economies induces these coun-tries to save less whereas the lower development of their financial mar-kets induces higher savings. So ultimately, which mechanism dominatesdepends on the relative importance of “growth differences” versus “fi-nancial differences.”

In addition to growth, another important difference between indus-trialized and emerging economies is that the latter are typically countriesthat are experiencing significant structural changes, which are oftenassociated with greater uncertainty at the individual level.15 Therefore,if we want to capture the differences between industrialized and emerg-ing economies that are relevant for savings, we should allow for threesources of heterogeneity: financial market development, economicgrowth, and income volatility.

We add heterogeneity in growth and income volatility to the three-country model examined above. An easy way to capture differences ingrowth rates is to assume that countries have different discount rates.If b is the discount factor for industrialized countries and the growthrate differential between emerging and industrialized countries is ,1 � gthen the discount factor of emerging countries is . Withjb p b/(1 � g)an annual growth differential of 3.5 percent and given the baseline pa-rameterization and , the discount factor for C3 is ˜b p 0.925 j p 2 b p

. In this case, if C1 and C2 grow at about 2 percent20.925/1.035 p 0.863per year, emerging countries (C3) grow at 5.5 percent per year. To accountfor the higher uncertainty faced by agents in emerging economies, weassume that the standard deviations of endowment and investment shocksin C3 are 50 percent higher than in C1 and C2.

Table 6 reports the steady-state statistics. Even if C3 grows faster thanthe other two countries, the combination of greater uncertainty andlower financial development induces agents in C3 to save more. As aresult, C3 accumulates a positive NFA position, and the composition ofits portfolio is tilted toward less risky and less profitable assets. In short,our key findings seem robust to the introduction of differences in growthand income volatility.

VII. Conclusion

This paper shows that international financial integration can lead tolarge and persistent global imbalances when countries differ in the de-

15 An indicator of this is that inequality tends to increase during phases of rapid growth.See Khan and Riskin (2001) and Naughton (2007). Also, several emerging economieshave experienced sudden stops after entering the global financial markets. The role playedby differences in the volatility of risk for the accumulation of foreign assets or reserveshas also been explored in Carroll and Jeanne (2008) and Durdu, Mendoza, and Terrones(2009).




TABLE 6Steady State in the Three-Country Economy with Heterogeneity in Financial

Development, Growth, and Income Volatility


C1 C2 C3 C1 C2 C3

Prices of productive assets 2.65 2.95 3.84 2.85 2.82 2.87Returns on productive

assets 5.63 5.05 3.60 5.10 5.10 5.81Standard deviation of

returns 7.17 6.44 19.51 4.14 4.16 14.13Interest rate 3.96 3.53 1.24 3.68 3.68 3.68Net foreign asset positions . . . . . . . . . �76.89 �.23 117.07

Productive assets . . . . . . . . . 29.68 29.54 �120.70Bonds . . . . . . . . . �106.57 �29.77 237.77

Note.—The heterogeneous parameters are , , ,f p (0.5, 0.5, 0) a p (�1, 0, 0) b p (0.925, 0.925, 0.863) D p (0.6,w

, , and . See also table 1.0.6, 0.9) D p (2.5, 2.5, 3.75) m p (0.3, 0.5, 0.2)z

gree of domestic financial development. Financial integration inducescountries with deeper financial markets to reduce savings and accu-mulate a large stock of net foreign liabilities in a long and gradualprocess. Financial heterogeneity also affects the composition of the port-folio of net foreign assets. Countries with deeper financial markets bor-row heavily from abroad and invest in high-return foreign risky assets.These patterns are consistent with the features of the global externalimbalances observed since the beginning of the 1980s. The model cangenerate these patterns as the outcome of financial integration in aworld in which the development of domestic financial markets is theonly source of cross-country heterogeneity.

The main implications of our analysis proved to be robust to (a)introducing alternative forms of financial development, (b) allowing forinternational diversification of individual risks, (c) considering resi-dence- or source-based enforcement of contracts, and (d) combiningdomestic financial heterogeneity with relatively large differences ingrowth rates and idiosyncratic income volatility. Thus, we conclude thatfinancial globalization among countries with heterogeneous domesticfinancial markets can be an important factor for explaining the largeexternal imbalances that have emerged across the United States, otherindustrial countries, and emerging economies.

Appendix A

Data

Emerging economies.—Argentina, Brazil, Chile, China, Colombia, Czech Repub-lic, Egypt, Hong Kong, Hungary, India, Indonesia, Israel, Jordan, Korea, Ma-laysia, Morocco, Pakistan, Peru, Philippines, Poland, Russia, Saudi Arabia, Sin-gapore, South Africa, Thailand, and Turkey.




Financial development indicators.—The IMF (2006) proposes an index of finan-cial market development for industrial countries. The index combines infor-mation from three core subindexes: an index of traditional bank intermediation,an index of new financial intermediation (i.e., intermediation through directmarket instruments, such as asset-backed securities and derivatives, and/or non-bank intermediaries, such as hedge funds), and an index of general character-istics of financial markets (stock market turnover, investor protection, bondmarket capitalization, etc.). Countries with a higher index undertake a largervolume of financial intermediation through direct market instruments and areviewed as having attained a higher degree of financial development.

Abiad et al. (2008) constructed an 82-country database of financial reformsfor both industrialized and emerging economies over the period 1973–2002,with seven dimensions of financial sector policies: (1) credit controls and highreserve requirements, (2) interest rate controls, (3) entry barriers, (4) stateownership in the banking sector, (5) capital account restrictions, (6) prudentialregulations and supervision of the banking sector, and (7) securities marketpolicies. The financial liberalization index in figure 1B is the average of thoseindicators.

Financial globalization index.—Chinn and Ito (2005) compiled an index of thedegree of capital account openness for 163 countries from 1970 to 2004. Theindex is based on binary dummy variables that codify the restrictions on cross-border financial transactions reported in the IMF’s Annual Report on ExchangeArrangements and Exchange Restrictions. The dummy variables reflect the fourmajor categories of restrictions: multiple exchange rates, restrictions on currentaccount transactions, restrictions on capital account transactions, and require-ments for the surrender of export proceeds. The index is the first standardizedprincipal component of these four variables, and it takes higher values for coun-tries that are more open to cross-border capital transactions. The indices forcountry groups are computed by averaging the individual country indices,weighted by GDP.

Foreign asset positions.—Lane and Milesi-Ferretti (2007) have constructed dataon gross and net foreign assets and liabilities, for different instruments, overthe period 1970–2004. The NFA positions are calculated by aggregating thedifferent assets and liabilities.

Appendix B

Set of Feasible Contingent Claims

Suppose that agents have the ability to divert part of their income. Diversion isobservable but not verifiable in a legal sense. If an agent diverts x, he or sheretains and the remaining part, fx, is lost. We allow f to be greater(1 � f)xthan one. This can be interpreted as a fine or additional punishment. A similarassumption is made in Castro, Clementi, and MacDonald (2004) in an environ-ment with information asymmetry.

Contracts are signed with financial intermediaries in a competitive environ-ment. Financial contracts are not exclusive, meaning that agents can alwaysswitch to another intermediary from one period to the other. The set of state-




contingent claims that an intermediary is willing to offer must be incentivecompatible.

Let be the value function for an agent with current realization ofV(s, a)t

shocks, , and current net worth, a. The net worth is before consump-s p (w, z)tion. After the contingent claims are chosen, the next period value isb(s )n

, where . In case of diversion, the agentnV(s , a(s )) a(s ) p w � z k � kP � b(s )t n n n n n t�1 n

would claim that the realizations of the endowment and productivity were thelowest levels, , and divert . In this process thens p (w , z ) w � w � (z � z )k1 1 1 n 1 n 1

agent retains and receives . Therefore, the netn(1 � f)[w � w � (z � z )k ] b(s )n 1 n 1 1

worth after diversion is

n nw � z k � (1 � f) 7 [w � w � (z � z )k ] � kP � b(s ) p1 1 n 1 n 1 t�1 1

na(s ) � (1 � f) 7 [w � w � (z � z )k ],1 n 1 n 1

and the value of diversion is

nV(s , a(s ) � (1 � f) 7 [w � w � (z � z )k ]).t n 1 n 1 n 1

Incentive compatibility requires that the following holds for all :n p 1, … , N

nV(s , a(s )) ≥ V(s , a(s ) � (1 � f) 7 [w � w � (z � z )k ]).t n n t n 1 n 1 n 1

It is important to emphasize that the financial intermediary can tell whetherthe agent is diverting, but there is no court that can verify this and force therepayment of the diverted funds. Compared to the standard model with infor-mation asymmetries, this assumption is convenient because it simplifies the con-tracting problem when shocks are persistent. Also convenient is the assumptionthat financial contracts are not exclusive and agents can switch to other inter-mediaries from one period to the other without a cost. This further limits thepunishments available to the current intermediary. Also notice that, althoughthe new level of wealth after diversion is verifiable when a new contract is signed,this does not allow the verification of diversion because the additional resourcescould derive from lower consumption in previous periods, which is not verifiable.The fraction of lost income f can be interpreted as the cost for hiding (makingnonverifiable) the diverted income and for hiding consumption. Again, theintermediary knows that the additional resources come from diversion, but itcannot legally prove it.

The last assumption is limited liability. Agents can renegotiate negative valuesof net worth and, therefore, . The agent’s problem reads asa(s ) ≥ 0n

′ ′ ′V(s, a) p max U(c) � b V (s , a(s ))g(s, s )�t t�1{ }′′ sc,k,b(s )




subject to

′ ′a p c � kP � b(s )q(s, s ),�t ′s

′ ′ ′ n ′a(s ) p w � z k � kP � b(s ),t�1

nV(s , a(s )) ≥ V(s , a(s ) � (1 � f) 7 [w � w � (z � z )k ]),t n n t n 1 n 1 n 1

a(s ) ≥ 0.n

Using standard arguments, we can prove that there is a unique solution andthe function is strictly increasing and concave in a.16 The strict mono-V(s, a)t

tonicity of the value function implies that the incentive-compatibility constraintcan be written as

na(s ) ≥ a(s ) � (1 � f) 7 [w � w � (z � z )k ]n 1 n 1 n 1

for all . This is the constraint we imposed on the original problem.n p 1, … , NWe arrived at this simple formulation of the enforcement constraints because

of the particular environment we considered. With an alternative assumptionof information asymmetries and persistent shocks, the characterization of theoptimal contract becomes more complicated. Because the qualitative propertiesare similar to the frictions considered here (see, e.g., Fernandes and Phelan2000), we opted for the simpler route.

Appendix C

Analytical Proofs

Proof of Proposition 1

In both economies we have that . Because with capital mobility¯R(k, z) p 1 � rt

there is a single worldwide interest rate, all agents employ the same input ofcapital . Therefore, the net position in the productive asset is zero. Wek p 1want to show that the interest rate is smaller than the intertemporal discountrate. Suppose, on the contrary, that . Under this condition agentsb(1 � r ) ≥ 1t

in C1 will have nonnegative consumption growth (see lemma 1) and agents inC2 will have positive consumption growth (see lemma 2). This implies thatworldwide consumption growth is positive, which cannot be an equilibriumbecause aggregate income is constant. Therefore, the equilibrium must satisfy

. Under this condition, agents in C1 will experience negative con-b(1 � r ) ! 1t

sumption growth (see again lemma 1) until the limited liability constraint (4)binds. Therefore, at some point, the net worth becomes zero for all agents.Because in C1 the net holding of productive assets is equal to the domesticendowment of one, the budget constraint becomes c � P �� b(w )q(w ,t t t�1 twt�1

. This implies ; that is, C1 borrows from C2w ) p 0 � b(w )q(w , w ) ! 0t�1 t�1 t t�1wt�1

(the NFA is negative). QED

16 The proof is facilitated by defining the variable . After the change of variablesnx p kis made, it can be easily proved that this is a standard concave problem.1/nk p x




Proof of Proposition 2

Suppose that . Under this condition agents in C1 will have nonneg-b(1 � r) ≥ 1ative consumption growth and agents in C2 will have strictly positive consump-tion growth (lemmas 1 and 2 apply also to the case with only investment shocks).This implies that worldwide consumption growth is positive, which cannot be asteady-state equilibrium. Therefore, . Under this condition agents inb(1 � r ) ! 1t

C1 will experience negative consumption growth (see again lemma 1) until thelimited liability constraint (4) binds. Therefore, at some point, the net worthbecomes zero for all agents. As in proposition 1, this implies that the NFAposition of C1 becomes negative.

To show that C1 has a positive net position in the productive asset, consideragain the first-order conditions (11)–(14). From these conditions we have that

in C1 and in C2. The monotonicity of with′ ′ER (k, z ) p 1 � r ER (k, z ) 1 1 � r Rt t t

respect to k implies that the productive asset used by agents in C1 is bigger thanthe productive asset used by agents in C2. Because the supply is the same, C1must own part of the productive asset of C2.

What remains to be shown is that for C1 the average return from the foreignproductive investment is higher than the cost of its foreign liabilities. Eventhough the marginal return from the productive asset is equalized to the interestrate, the concavity of the production function implies that the average returnis higher than the interest rate. This compensates the managerial capital. QED

Appendix D

Computational Procedure

We show first that the economy with contingent claims is equivalent to an econ-omy in which contingent claims are not allowed but agents face a differentprocess for the exogenous shocks. We can then solve the equivalent economyin which the agents’ problem is a standard portfolio choice over riskless andrisky assets. After showing this, we describe the computational procedures usedto solve for the steady-state and transitional equilibria.

A. Equivalent Economy

Let be the expected next period value of contingent claims, that is,¯ ¯b b pt t

. Then a contingent claim can be rewritten as ¯� b(s )g(s , s ) b(s ) p b �t�1 t t�1 t�1 tst�1

, where . The variable can be interpreted as a¯x(s ) � x(s )g(s , s ) p 0 bt�1 t�1 t t�1 tst�1

noncontingent bond and is the pure insurance component of contingentx(s )t�1

claims. The law of motion for the next period assets becomes

I

j 1�n n ¯a(s ) p w � (k P � z A k ) � b � x(s ). (D1)�t�1 t�1 j,t t�1 j,t�1 j,t j,t t t�1jp1




Because agents will choose as much insurance as possible, the incentive-compatibility constraint will be satisfied with equality, that is,

I

1�n na(s ) p a(s ) � (1 � f) 7 w � w � (z � z )A k .�n 1 n 1 j,n j,1 j,t j,t[ ]jp1

Using the law of motion for a, we can write the constraint as

I

1�n nx(s ) � x(s ) p �f 7 w � w � (z � z )A k ,�n 1 n 1 j,n j,1 j,t j,t[ ]jp1

which must hold for all . The variables must also satisfy then � {2, … , N } x(s )n

zero-profit condition, that is,

x(s )g(s , s ) p 0.� n t nn

Therefore, we have N conditions and N unknowns. We can then solve for allthe N values of . The solution can be written asxn

I

1�n nx(s ) p �f 7 W (s ) � f 7 Z (s ) 7 A k ,�n n t j,n t j,t j,tjp1

where and are exogenous variables defined asW (s ) Z (s )n t j,n t

W (s ) p w � g(s , s )w ,�n t n t l ll

Z (s ) p z � g(s , s )z .�j,n t j,n t l j,ll

These variables depend on the current shocks because they affect the probabilitydistribution for the next period shocks.

Define the following variables:

w (s ) p w � f 7 W (s ),n t n n t

z (s ) p z � f 7 Z (s ).j,n t j,n j,n t

These are transformations of the shocks. Using the transformed shocks, we canwrite the law of motion for next period assets as

I

j 1�n n ¯˜ ˜a(s ) p w (s ) � [k P � z (s ) 7 A k ] � b .�n n t j,t t�1 j,n t j,t j,t tj

Therefore, when we use the transformed shocks and , it is as if agents˜ ˜w (s ) z (s )n t j,n t

choose only noncontingent claims. Then the problem becomes a standard port-folio choice between risky assets, , and a riskless asset, . Differences in fi-¯k bj,t t

nancial development are captured by differences in the stochastic properties ofthe transformed shock. So, for example, if , we go back to the originalf p 0shock because contingent claims are not feasible. If and shocks are i.i.d.,f p 1the transformed shock becomes a constant. We are in the case of full insurance.Intermediate values of f allow only for partial insurance. In the computationwe will solve the portfolio choice in the transformed model.




B. Steady-State Equilibrium

1. Choose a grid for asset holdings a.

2. Guess the steady-state interest rate, r, and the prices .j I{P }jp1

3. Using the first-order conditions, solve for the optimal portfolio choices ateach grid point of a and for each s by iterating on the policy rules. Thesolutions at each grid point are joined with piecewise linear functions.

4. Find the steady-state distribution of agents using the decision rules andcompute the clearing conditions for the risky and riskless assets.

5. Update the guesses for the interest rate and the prices of the productiveassets (step 2) until the market-clearing conditions are satisfied.

C. Transitional Equilibrium

1. Solve for the initial and final steady states (autarky and mobility).

2. Choose the number of transition periods T. This number should be suffi-ciently large to allow the economy to reach, approximately, the new steadystate in T periods.

3. Guess transition sequences for the interest rates, , and for the priceT{r }t tp1

of the productive assets, . The final prices are set to thej I T j I{{P } } {P }t jp1 tp1 T�1 jp1

steady-state values with mobility found in step 1.4. Using the first-order conditions, solve for the optimal portfolio choices

backward starting from T. This provides the sequence of optimal decisionrules at .t p 1, 2, … , T

5. Using the optimal decision rules, find the sequence of distributions andcompute the market-clearing conditions at time .t p 1, 2, … , T

6. Update the guess for the sequences of the interest rates and the prices ofthe productive assets (step 3) until the market-clearing conditions are sat-isfied for each .t p 1, 2, … , T

References

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Documents

Financial Integration, Financial Development, and Global Imbalances